Highest Common Factor of 770, 177, 107 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 770, 177, 107 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 770, 177, 107 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 770, 177, 107 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 770, 177, 107 is 1.
HCF(770, 177, 107) = 1
HCF of 770, 177, 107 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 770, 177, 107 is 1.
Highest Common Factor of 770,177,107 is 1
Step 1: Since 770 > 177, we apply the division lemma to 770 and 177, to get
770 = 177 x 4 + 62
Step 2: Since the reminder 177 ≠ 0, we apply division lemma to 62 and 177, to get
177 = 62 x 2 + 53
Step 3: We consider the new divisor 62 and the new remainder 53, and apply the division lemma to get
62 = 53 x 1 + 9
We consider the new divisor 53 and the new remainder 9,and apply the division lemma to get
53 = 9 x 5 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 770 and 177 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(53,9) = HCF(62,53) = HCF(177,62) = HCF(770,177) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 107 > 1, we apply the division lemma to 107 and 1, to get
107 = 1 x 107 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 107 is 1
Notice that 1 = HCF(107,1) .
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Frequently Asked Questions on HCF of 770, 177, 107 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 770, 177, 107?
Answer: HCF of 770, 177, 107 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 770, 177, 107 using Euclid's Algorithm?
Answer: For arbitrary numbers 770, 177, 107 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
